Physics and Financial Economics (1776-2011) Inter-breeding ...

Princeton University Press (2003)

Physics and Financial Economics (1776-2011) Inter-breeding, Discoveries and Open Problems

D. SornetteProfessor of Entrepreneurial Risks at ETH Zurich

Professor of Finance at the Swiss Finance Institute

Director of the Financial Crisis Observatory

Founding member of the Risk Center at ETH Zurich (June 2011) (www.riskcenter.ethz.ch)

Professor of Geophysics associated with the Department of Earth Sciences (D-ERWD), ETH Zurich

Professor of Physics associated with the Department of Physics (D-PHYS), ETH Zurich

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• Collective dynamics and organization of social agents (Commercial sales,YouTube, Open source softwares, Cyber risks)

• Agent-based models of bubbles and crashes, credit risks, systemic risks

• Prediction of complex systems, stock markets, social systems

• Asset pricing, hedge-funds, risk factors…

• Human cooperation for sustainability

• Natural and biological hazards (earthquakes, landslides, epidemics, critical illnesses…)

D-MTEC Chair of Entrepreneurial RisksProf. Dr. Didier Sornette www.er.ethz.ch

price

time

Bubbles

Dynamics of success

(3 guest-professors, 5 foreign associate professors,3 post-docs, 3 senior researchers, 12 PhD students, ~12 Master students/year)

Adam Smith “Inquiry into the Nature and Causes of the Wealth of Nations” (1776)

•Francis Edgeworth and Alfred Marshall (1890) develop the concept of equilibrium

•“everything in the economy affects everything else”

•Vilfredo Pareto (1897): power law distribution of incomes

•Louis Bachelier (1900): random walk model of Paris stock market and solution of diffusion equation

•Benoit Mandelbrot (1963) proposes heavy-tailed distributions (Levy stable laws) for the pdf of cotton returns

•initially supported by Merton Miller, Eugene Fama, and Richard Roll (Chicago), Paul Samuelson (MIT), and Thomas Sargent (Carnegie Mellon), but opposition from Paul Cootner and Clive Granger;

•distributions of returns are becoming closer to the Gaussian law at timescales larger than one month.

•Isaac Newton Philosophiae Naturalis PrincipiaMathematica (1687) [(novel at the time) notion of causative forces]

•Clerk Maxwell and Ludwig Boltzmann (1871-1875): equilibrium in gases

•mean-field theory or self-consistent effective medium methods

•distribution of event sizes (earthquakes, avalanches, landslides, storms, forest fires, solar flares, commercial sales, war sizes, ...)

•Einstein (1905): theory of Brownian motion

•Benoit Mandelbrot (1977): Fractals

•Much of the efforts in the econophysics (1993-2000s) refined the Levy hypothesis into

ECONOMICS PHYSICS

pdf(r) ∼ 1/r3>

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ECONOMICS PHYSICS

Adam Smith (1776)“Inquiry into the Nature and Causes of the Wealth of Nations”

Isaac Newton (1687)Philosophiae Naturalis Principia Mathematica

notion of causative forces (novel at the time)

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ECONOMICS PHYSICS

Francis Edgeworth and Alfred Marshall (1890) develop the concept of equilibrium

“everything in the economy affects everything else”

Clerk Maxwell and Ludwig Boltzmann (1871-1875)equilibrium in gases

mean-field theory or self-consistent effective medium methods

Equilibrium

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ECONOMICS PHYSICS

Vilfredo Pareto (1897)power law distribution of incomes

distribution of event sizes (earthquakes, avalanches, landslides, storms, forest fires, solar flares, commercial sales, war sizes, ...)

Non-Gaussian heavy tailed distributions

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ECONOMICS PHYSICS

Louis Bachelier (1900)random walk model of Paris stock market and solution of diffusion equation

Einstein (1905)theory of Brownian motion

Theory of random walks and diffusion equation

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ECONOMICS PHYSICSBenoit Mandelbrot (1963) Heavy-tailed distributions (Levy stable laws) for the pdf of cotton returns

initially supported by Merton Miller, Eugene Fama, and Richard Roll (Chicago), Paul Samuelson (MIT), and Thomas Sargent (Carnegie Mellon), but opposition from Paul Cootner and Clive Granger

distributions of returns are becoming closer to the Gaussian law at timescales larger than one month.

Benoit Mandelbrot (1977)Fractals

Much of the efforts of econophysicists (1993-2000s) refined the Levy hypothesis into

self-similaritypdf(r) ∼ 1/r3

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ECONOMICS PHYSICS

-Paul Krugman (1996)“Self-organizing economy” -Brian Arthur (1992)Induction, out-of-equilibrium-Santa Fe Institute (1994-...)

P. W. Anderson (1957)“More is different” (1972)-Out-of-Equilibrium-frozen heterogeneity (spinglasses, glasses, proteins)

Out-of-equilibrium, frozen heterogeneity,Self-organization, phase transitions ....

ETH Risk Initiative

ETHRisk Center10 Founding ChairsIntegrative

RiskManagement

(Bommier)

IRM Focus banking(pending)

Risk & InsuranceEconomics

(hiring started)

Risk LabProfessor Embrechts(13 Research Groups)Postgraduate Program in „Advanced Studies in Finance“

HazNETHNetwork for Natural Hazards Postgraduate Program14 Professorships

Reliability/RiskEngineeringSucessor in Lab for Safety Analysis1 Professorship

IBK / IBSBuilding materialsStructural Engineering5 ProfessorshipsCSS

Center for Security StudiesProf. Wenger30 researchers

Vision: World-leading, inspiring nucleus for integrative risk research and teaching

KOFSwiss economics research (business cycles)2 Professorships

Par

tner

ship

Cou

ncil

Pro

ject

Fun

d

MTECManagement, Techn, Economics20 Professorships

GESSConflict Research, Behavioral StudiesModeling Sozio-Economi.6 Professorships

ZISCZurich Information Security Center4 Professorships

A partial lists of achievements of Econophysics

• scaling laws, “universality” • agent-based models, induction, evolutionary models [1, 9, 11, 21],• minority games [8], • option theory for incomplete markets [4, 6], • “string theory” of interest rate curves [5, 38], • theory of Zipf law and its economic consequences [12, 13, 27], • theory of large price fluctuations [14], • theory of bubbles and crashes [17, 22, 40],• random matrix theory applied to covariance of returns [20, 36, 37], • methods and models of dependence between financial assets [25,

43].

15G. Daniel and D. Sornette, Econophysics: historical perspectives, in the Encyclopedia of Quantitative Finance, edited by Rama Cont (www.wiley.com/go/eqf), Section: History of Quantitative Modeling (1st section out of 21), edited by Perry Mehrling and Murad Taqqu (http://arXiv.org/abs/0802.1416)

A partial lists of achievements of Econophysics

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Need for econophysics results and insights to be known

Strategy: team up with economists to develop rigorousstatistical approachs and publish in top financial or economic journals

Reach beyond physics and marry with other disciplines

Physics is no-more the Queen of sciences.

Examples: role of financial firms to influence the rest of theeconomy; networks of networks and fragility versus robustness; critical phenomena...

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(i) the fluctuation-susceptibility theorem transforms intoa remarkable classification of financial volatility shocks (endogenous versus exogenous),

(ii) the Ising model of phase transitions can be generalizedto model the stylized facts of financial markets,

(iii) the concepts of collective phenomena and phasetransitions (with spontaneous symmetry breaking) help understand financial bubbles and their following crashes,

(iv) the mathematics of quantum physics provides a new quantum decision theory solving the known paradoxes.

FOUR EXAMPLES

Guidelines from Physics: perturb and study the response

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EXO:Drag resistanceunder an external force

ENDO: Random walk

(Einstein, 1905)

r2=2d Dt

D=kBT/γ

Fluctuation-dissipation theorem far from equilibrium is not expected to hold

Externally imposed perturbations may be different from spontaneous fluctuations (external fluctuations lie outside the complex attractor)

Attractor of dynamics may exhibit bifurcations

D. Ruelle, Physics Today, May 2004

(Roehner and Sornette, 2004)

The method of critical events in economics and social sciences

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Daily number of donations following the Asian Tsunami of December 26, 2004

(Crane, Schweitzer and Sornette, 2009)

Volatility

D. Sornette, Y. Malevergne and J.F. Muzy Volatility fingerprints of large shocks: Endogeneous versus exogeneous, Risk Magazine(http://arXiv.org/abs/cond-mat/0204626)

October 1987 crash:totally different mechanism

(Multifractal Random Walk model)

where

Interplay between-long memory-exponential

D. Sornette, Y. Malevergne and J.F. Muzy, Volatility fingerprints of large shocks: Endogeneous versus exogeneous, Risk 16 (2), 67-71 (2003) (http://arXiv.org/abs/cond-mat/0204626)

Real Data and Multifractal Random Walk model

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Endogenous versus ExogenousExtinctions -meteorite at the Cretaceous/Tertiary KT boundary -volcanic eruptions (Deccan traps) -self-organized critical eventsFinancial crashes -external shock -self-organized instabilityImmune system -external viral or bacterial attack - “ internal” (dis-)organizationBrain (learning) -external inputs -internal self-organization and reinforcements (role of sleep)

Recovery after wars? -internally generated (civil wars) -externally generated

Aviation industry recession -September 11, 2001 -structural endogenous problems

Volatility bursts in financial time series -external shock -cumulative effect of “small” news

Commercial success and sales -Ads -epidemic network Social unrests -triggering factors -rotting of social tissue

Discoveries -serendipity -maturation

Parturition -mother/foetus triggered? -mother-foetus complex?

Earthquakes -tectonic driving -triggering

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FOUR EXAMPLES

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Imitation

-Imitation is considered an efficient mechanism of social learning.

- Experiments in developmental psychology suggest that infants use imitation to get to know persons, possibly applying a ‘like-me’ test (‘persons which I can imitate and which imitate me’).

- Imitation is among the most complex forms of learning. It is found in highly socially living species which show, from a human observer point of view, ‘intelligent’ behavior and signs for the evolution of traditions and culture (humans and chimpanzees, whales and dolphins, parrots).

- In non-natural agents as robots, tool for easing the programming of complex tasks or endowing groups of robots with the ability to share skills without the intervention of a programmer. Imitation plays an important role in the more general context of interaction and collaboration between software agents and human users.

Humans Appear Hardwired To Learn By 'Over-Imitation'ScienceDaily (Dec. 6, 2007) — Children learn by imitating adults--so much so that they will rethink how an object works if they observe an adult taking unnecessary steps when using that object.

Shiller (2000)

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Disorder : K small

OrderK large

Critical:K=criticalvalue

Renormalization group:Organization of thedescription scale by scale

si(t + 1) = sign

K�

j∈Ni

sj + �i

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Imitation News

1. β<0: rational agents

• β>0: over-confident agents

Didier Sornette and Wei-Xing Zhou, Physica A 370 (2), 704-726 (2006)

(generalizes Carlos Pedro Gonçalves, who generalized Johansen-Ledoit-Sornette)

β: propensity to be influenced by the felling of others

Privateinformation

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Bubbles and crashes

D. Sornette and W.-X. ZhouPredictability of Large Future Changes in major financial indices,International Journal of Forecasting 22, 153-168 (2006)

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Aggregation of information

G. Harras and D. Sornette, Endogenous versus exogenous origins of financial rallies and crashes in an agent-based model with Bayesian learning and imitation, J. Economic Behavior and Organization (2008) (http://arXiv.org/abs/0806.2989

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News impact

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FOUR EXAMPLES

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Various Bubbles and Crashes

Each bubble has been rescaled vertically and translatedto end at the time of the crash

time

price

40

Hong-Kong

Red line is 13.8% per year: but The market is never following the average

growth; it is either super-exponentiallyaccelerating or crashing

Patterns of price trajectory during 0.5-1 year before each peak: Log-periodic power law

Textbook example of a series of superexponential acceleration followed by crashes

41Multi-dimensional generalization: multi-variate positive feedbacks

Positive feedbacks and finite-time singularity

with

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Super-exponential growth

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Mechanisms for positive feedbacks in the stock market

• Technical and rational mechanisms 1. Option hedging2. Insurance portfolio strategies3. Trend following investment strategies4. Asymmetric information on hedging strategies

• Behavioral mechanisms: 1. Breakdown of “psychological Galilean invariance”2. Imitation(many persons)

a) It is rational to imitateb) It is the highest cognitive task to imitatec) We mostly learn by imitationd) The concept of “CONVENTION” (Orléan)

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DISCRETE HIERARCHYOF THE AGENT NETWORK

Co-evolution of brain size and group size (Why do we have a big Brain?)

Interplay between nonlinear positive and negative feedbacks and inertia

Discrete scale invariance Complex fractal dimension Log-periodicity

Presentation of three different mechanisms leading to discrete scale invariance, discrete hierarchies and log-periodic signatures

Kimmo Soramäki, Morten L. Bech, Jeffrey Arnold, Robert J. Glass, and Walter E. Beyeler, Physica A 379, 317-333 (2006)

network topology of the interbank payments transferred betweencommercial banks over the Fedwire® Funds Service

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Didier Sornette, Ryan Woodard, Peter Cauwels, Vladimir Filimonov, Wanfeng Yan, Qunzhi Zhang, Wei-Xing Zhou

Chinese bubble(Aug 2009)

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•Hypothesis H1: financial (and other) bubbles can be diagnosed in real-time before they end.

•Hypothesis H2: The termination of financial (and other) bubbles can be bracketed using probabilistic forecasts, with a reliability better than chance.

The Financial Bubble Experimentadvanced diagnostics and forecasts of bubble terminations

Positive feedbacks of higher return anticipation ✴Super exponential price ✴Power law “Finite-time singularity”

Negative feedback spirals of crash expectation ✴Accelerating large-scale financial volatility ✴Log-periodic discrete scale-invariant patterns

Methodology for diagnosing bubbles

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“New Economy”: ICT

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Real-estate in the UK

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Real-estate in the USA

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bubble peaking in Oct. 2007

Source: R. Woodard (FCO, ETH Zurich)

53Typical result of the calibration of the simple LPPL model to the oil price in US$ in shrinking windows with starting dates tstart moving up towards the common last date tlast = May 27, 2008.

2006-2008 Oil bubble

D. Sornette, R. Woodard and W.-X. Zhou, The 2006-2008 Oil Bubble and Beyond,Physica A 388, 1571-1576 (2009)(arXiv.org/abs/0806.1170)

Speculation vs supply-demand

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FOUR EXAMPLES

Partial list of problems with standard Utility theory

• Allais paradox (Compatibility violation: Several choices are not compatible with utility theory)

• Ellsberg paradox (uncertainty aversion)

• Kahneman-Tversky paradox (invariance violation)

• Rabin paradox (payoff size effects)

• Disjunction effect (violation of the sure-thing principle)

• Conjunction fallacy (violation of probability theory)

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“Bounded rationality”• In 1957, Herbert Simon described

the principle of “bounded rationality” - Nobel Prize in 1978:

“The capacity of the human mind for formulating and solving complex problems is very small compared with the size of the problem whose solution is required for objectively rational behavior in the real world, or even for a reasonable approximation to such objective rationality.”

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=>Towards a fundamental theory of human decision making

(triune brain: reptilian, emotional, rational)

Quantum Decision Theory?

V.I. Yukalov and D. SornetteProcessing Information in Quantum Decision Theory,Entropy 11, 1073-1120 (2009)

V.I. Yukalov and D. SornetteEntanglement Production in Quantum Decision Making,Physics of Atomic Nuclei 73 (3), 559-562 (2010).

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● Novel approach to decision making is developed based on a complex Hilbert space over a lattice of composite prospects.•Risk of loss and uncertainty are taken into account. •Decisions are probabilistic and depend on state of mind that can be changed or framed.● Paradoxes of classical decision theory are explained.● Good quantitative agreement with empirical data.● Conjunction fallacy is a sufficient condition for disjunction effect.

“Nature” is more imaginative than mathematicians, economists or... econophysicists

Questions and Strategy for the future

Risks Interconnection Map (RIM) 2010

Source: World Economic Forum 2010

(10-year time horizon)

IMMENSE PROGRESS and INNOVATIONFINANCIAL SYSTEM

Financial innovations have fosteredthe use of capital for •economic development, •welfare, •education...

FOOD AND HEALTHCARE•Decrease of newborn and infantmortality•Height as a proxy for health

Unicef data

1800 2000 Baten (2006)

Height

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Loss of “Fiduciary Principle”ʻno man can serve two mastersʼ(J. Bogle, former CEO Vanguard group, JPM 2009)

“Legal relationship of confidence or trust between two parties”

The issue of “moral relativism”

Moral hazard

Incentives

Loss of “Hippocratic oath”ʻnil nocereʼ

Fundamental conflict of interest to keep us “marginally ill”

Maximizing share-holder value

Rational focus on short-term in the presence of large risks and uncertainties

CONFLICTS OF INTERESTS

FINANCIAL SYSTEM FOOD AND HEALTHCARE

HUMAN INTRINSIC WEAKNESSES

The ScientistVolume 20 | Issue 2 | Page 51

FINANCIAL SYSTEM

The illusionary quest of society-at-large, pensions funds, mutual funds... to gain more than 2% return in real terms (above inflation)

The “gambling society” (stardom culture, emphasis on “luck”) vs work and risk management

FOOD AND HEALTHCARE

The illusionary syndrome for “blue pills and red pills”...

Principle of least effort (Zipf, 1949)

Principle of immediate or short-term gratification (large “discount rate”)

People simply fail to do what is best even for themselves, in the face of good, freely available information.

The root cause of the crisisis our illusion on financialsolution to growth (high returns, above GDP growth)

The root cause of the cominghealthcare crisis is our illusionin technical / medical solutions.

HUMAN INTRINSIC WEAKNESSES

The ScientistVolume 20 | Issue 2 | Page 51

FOOD AND HEALTHCARE•The food industry exploits our weakness (addictive and/or compensatory nature of some foods). •The pharmaceutical industry exploits our illusions for simple solutions to health problems.

Fundamental failure to grasp the SYSTEM nature of the problems:Instead, one problem => one proximate solution: THIS IS WRONG!

FINANCIAL SYSTEM•Bankers are sellers of dreams.•Bankers exploit our illusions and cognitive limitations... like casinos and lotteries...

Tversky, Amos and Craig R. Fox, “Weighing Risk and Uncertainty”, Psychological Review, CXLIX (1995), 269-83.

• Public goods (individual cost for benefit to the group) (recycling, hybrid car, valor in combat, voting, donating blood,...)

• Tragedy of the commons (shared resource gives benefit to personal use and distributed losses) (cows in shared pastures, Air, Water, Scenery, global warming, pollution...)

–Earth renewable services are exogenous to the economic costs and decision processes

• Externalities: pollution• Market failures: asymmetric information

Cooperation and coordination problems

Theory and practice of human cooperation?

-Financial innovations, High Frequency Trading... are justified by improved LIQUIDITY

=> do we need so much liquidity?



Welfare

Liquidity

I



Welfare

Liquidity

I

II



Welfare

Liquidity

I

II

III

Questions and Strategy for the future

from post-mortem data analysis

to

real-time hand-on experiments, trading and design

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At present: most exciting progresses at the boundary between economics and the biological, cognitive, and behavioral sciences.

Physics has still a role to play as a unifying framework full of concepts and tools to deal with the complex.

The modeling skills of physicists explain their impressive number in investment and financial institutions (data-driven approach coupled with a pragmatic sense of theorizing)

KEY CHALLENGE: true inter-disciplinarity by “marriage”

D-MTEC Chair of Entrepreneurial Risks

Prof. Dr. Didier Sornette www.er.ethz.ch

"It is impossible to produce a superior performance unless you do something different from the majority".Sir John Templeton.

"How many things are looked on as quite impossible until they have been actually effected?" (Pliny the Elder, 1st c. AD: Natural History, Book VII, section 6)

Everybody knew it is impossible. He/She did not know it.He/She did it.

Entrepreneurial-Scientific spirit

Physics and Financial Economics (1776-2011) Inter-breeding ...

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